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3 years ago

10

Bert’s cab company charges $1.00 plus an additional $3.00 per mile for a ride. Madeline’s cab company charges $3.00 plus an addi

tional $2.00 per mile for a ride. At what distance, in miles, will the cost be the same for both companies? *

1 answer:

katrin [286]3 years ago

5 0

Answer:

20 miles

Step-by-step explanation:

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<em><u>Explanation</u></em>

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According to the diagram below....

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Length of the side AB (c) $= \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}$

We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...

$cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree$

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